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arXiv · 1307.2684

The threshold for collapsibility in random complexes

Lior Aronshtam·Nati Linial
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Abstract

In this paper we determine the threshold for collapsibility in the probabilistic model $X_d(n,p)$ of $d$-dimensional simplicial complexes. A lower bound for this threshold $p=\frac{c_d}{n}$ was established in \cite{ALLM}. Here we show that this is indeed the correct threshold. Namely, for every $c>c_d$, a complex drawn from $X_d(n,\frac{c}{n})$ is asymptotically almost surely not collapsible.

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Lior Aronshtam, Nati Linial. 2013-07-10. The threshold for collapsibility in random complexes. https://arxiv.org/abs/1307.2684

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